THE LOWER CENTRAL AND DERIVED SERIES OF THE BRAID GROUPS OF THE SPHERE

In this paper, we determine the lower central and derived series for the braid groups of the sphere. We are motivated in part by the study of Fadell-Neuwirth short exact sequences, but the problem is important in its own right. The braid groups of the 2-sphere S(2) were studied by Fadell, Van Buskirk and Gillette during the 1960s, and are of particular interest due to the fact that they have torsion elements (which were characterised by Murasugi). We first prove that for all n epsilon N, the lower central series of the n-string braid group B(n)(S(2)) is constant from the commutator subgroup onwards. We obtain a presentation of Gamma(2)(Bn(S(2))), from which we observe that Gamma(2)(B(4)(S(2))) is a semi-direct product of the quaternion group Q(8) of order 8 by a free group F(2) of rank 2. As for the derived series of Bn(S(2)), we show that for all n >= 5, it is constant from the derived subgroup onwards. The group Bn(S(2)) being finite and soluble for n <= 3, the critical case is n = 4 for which the derived subgroup is the above semi-direct product Q(8) (sic) F(2). By proving a general result concerning the structure of the derived subgroup of a semi-direct product, we are able to determine completely the derived series of B(4)(S(2)) which from (B(4)(S(2)))(4) onwards coincides with that of the free group of rank 2, as well as its successive derived series quotients.

COUNTABLE GROUPS OF ISOMETRIES ON BANACH SPACES

A group G is representable in a Banach space X if G is isomorphic to the group of isometrics on X in some equivalent norm. We prove that a countable group G is representable in a separable real Banach space X in several general cases, including when G similar or equal to {-1,1} x H, H finite and dim X >= vertical bar H vertical bar or when G contains a normal subgroup with two elements and X is of the form c(0)(Y) or l(p)(Y), 1 <= p < +infinity. This is a consequence of a result inspired by methods of S. Bellenot (1986) and stating that under rather general conditions on a separable real Banach space X and a countable bounded group G of isomorphisms on X containing -Id, there exists an equivalent norm on X for which G is equal to the group of isometrics on X. We also extend methods of K. Jarosz (1988) to prove that any complex Banach space of dimension at least 2 may be renormed with an equivalent complex norm to admit only trivial real isometries, and that any complexification of a Banach space may be renormed with an equivalent complex norm to admit only trivial and conjugation real isometrics. It follows that every real Banach space of dimension at least 4 and with a complex structure may be renormed to admit exactly two complex structures up to isometry, and that every real Cartesian square may be renormed to admit a unique complex structure up to isometry.

Temperature effects on the oscillatory electro-oxidation of methanol on platinum

We report in this paper the effect of temperature on the oscillatory electro-oxidation of methanol on polycrystalline platinum in aqueous sulfuric acid media. Potential oscillations were studied under galvanostatic control and at four temperatures ranging from 5 to 35 degrees C. For a given temperature, the departure from thermodynamic equilibrium does not affect the oscillation period and results in a slight increase of the oscillation amplitude. Apparent activation energies were also evaluated in voltammetric and chronoamperometric experiments and were compared to those obtained under oscillatory conditions. In any case, the apparent activation energies values fell into the region between 50 and 70 kJ mol(-1). Specifically under oscillatory conditions an apparent activation energy of 60 +/- 3 kJ mol(-1) and a temperature coefficient q(10) of about 2.3 were observed. The present findings extend our recently published report (J. Phys. Chem. A, 2008, 112, 4617) on the temperature effect on the oscillatory electro-oxidation of formic acid. We found that, despite the fact that both studies were carried out under similar conditions, unlike the case of formic acid, only conventional, Arrhenius, dynamics was observed for methanol.

The role of the steps in the cleavage of the C-C bond during ethanol oxidation on platinum electrodes

Ethanol oxidation has been studied on stepped platinum single crystal electrodes in acid media using electrochemical and Fourier transform infrared (FTIR) techniques. The electrodes used belong to two different series of stepped surfaces: those having (111) terraces with (100) monoatomic steps and those with (111) terraces with (110) monoatomic steps. The behaviors of the two series of stepped surfaces for the oxidation of ethanol are very different. On the one hand, the presence of (100) steps on the (111) terraces provides no significant enhancement of the activity of the surfaces. On the other hand, (110) steps have a double effect on the ethanol oxidation reaction. At potentials below 0.7 V, the step catalyzes the C-C bond cleavage and also the oxidation of the adsorbed CO species formed. At higher potentials, the step is not only able to break the C-C bond, but also to catalyze the oxidation of ethanol to acetic acid and acetaldehyde. The highest catalytic activity from voltammetry for ethanol oxidation was obtained with the Pt(554) electrode.

Surface structure effects on the electrochemical oxidation of ethanol on platinum single crystal electrodes

Ethanol oxidation has been studied on Pt(111), Pt(100) and Pt(110) electrodes in order to investigate the effect of the surface structure and adsorbing anions using electrochemical and FTIR techniques. The results indicate that the surface structure and anion adsorption affect significantly the reactivity of the electrode. Thus, the main product of the oxidation of ethanol on the Pt(111) electrode is acetic acid, and acetaldehyde is formed as secondary product. Moreover, the amount of CO formed is very small, and probably associated with the defects present on the electrode surface. For that reason, the amount of CO(2) is also small. This electrode has the highest catalytic activity for the formation of acetic acid in perchloric acid. However, the formation of acetic acid is inhibited by the presence of specifically adsorbed anions, such as (bi) sulfate or acetate, which is the result of the formation of acetic acid. On the other hand, CO is readily formed at low potentials on the Pt(100) electrode, blocking completely the surface. Between 0.65 and 0.80 V, the CO layer is oxidized and the production of acetaldehyde and acetic acid is detected. The Pt(110) electrode displays the highest catalytic activity for the splitting of the C-C bond. Reactions giving rise to CO formation, from either ethanol or acetaldehyde, occur at high rate at any potential. On the other hand, the oxidation of acetaldehyde to acetic acid has probably the lower reaction rate of the three basal planes.

Complex kinetics, high frequency oscillations and temperature compensation in the electro-oxidation of ethylene glycol on platinum

Despite the fact that the majority of the catalytic electro-oxidation of small organic molecules presents oscillatory kinetics under certain conditions, there are few systematic studies concerning the influence of experimental parameters on the oscillatory dynamics. Of the studies available, most are devoted to C1 molecules and just some scattered data are available for C2 molecules. We present in this work a comprehensive study of the electro-oxidation of ethylene glycol on polycrystalline platinum surfaces and in alkaline media. The system was studied by means of electrochemical impedance spectroscopy, cyclic voltammetry, and chronoamperometry, and the impact of parameters such as applied current, ethylene glycol concentration, and temperature were investigated. As in the case of other parent systems, the instabilities in this system were associated with a hidden negative differential resistance, as identified by impedance data. Very rich and robust dynamics were observed, including the presence of harmonic and mixed mode oscillations and chaotic states, in some parameter region. Oscillation frequencies of about 16 Hz characterized the fastest oscillations ever reported for the electro-oxidation of small organic molecules. Those high frequencies were strongly influenced by the electrolyte pH and far less affected by the EG concentration. The system was regularly dependent on temperature under voltammetric conditions but rather independent within the oscillatory regime.

Bulk structures of PtO and PtO(2) from density functional calculations

Platinum plays an important role in catalysis and electrochemistry, and it is known that the direct interaction of oxygen with Pt surfaces can lead to the formation of platinum oxides (PtO(x)), which can affect the reactivity. To contribute to the atomistic understanding of the atomic structure of PtO(x), we report a density functional theory study of the atomic structure of bulk PtO(x) (1 <= x <= 2). From our calculations, we identified a lowest-energy structure (GeS type, space group Pnma) for PtO, which is 0.181 eV lower in energy than the structure suggested by W. J. Moore and L. Pauling [J. Am. Chem. Soc. 63, 1392 (1941)] (PtS type). Furthermore, two atomic structures were identified for PtO(2), which are almost degenerate in energy with the lowest-energy structure reported so far for PtO(2) (CaCl(2) type). Based on our results and analysis, we suggest that Pt and O atoms tend to form octahedron motifs in PtO(x) even at lower O composition by the formation of Pt-Pt bonds.

Nanogravimetric and voltammetric studies of a Pt-Rh alloy surface and its behavior for methanol oxidation

This paper describes the preparation of a Pt-Rh alloy surface electrodeposited on Pt electrodes and its electrocatalytic characterization for methanol oxidation. The X-ray photoelectronic spectroscopy ( XPS) results demonstrate that the surface composition is approximately 24 at-% Rh and 76 % Pt. The cyclic voltammetry (CV) and electrochemical quartz crystal (EQCN) results for the alloy were associated, for platinum, to the well known profile in acidic medium. For Rh, on the alloy, the generation of rhodium hydroxide species (Rh(OH)(3) and RhO(OH)(3)) was measured. During the successive oxidation-reduction cycles the mass returns to its original value, indicating the reversibility of the processes. It was not observed rhodium dissolution during the cycling. The 76/24 at % Pt-Rh alloy presented singular electrocatalytic activity for methanol electrooxidation, which started at more negative potentials compared to pure Pt (70 mV). During the sweep towards more negative potentials, there is only weak CO re-adsorption on both Rh and Pt-Rh alloy surfaces, which can be explained by considering the interaction energy between Rh and CO.

k(0)-INAA for determining chemical elements in bird feathers

The k(0)-method instrumental neutron activation analysis (k(0)-INAA) was employed for determining chemical elements in bird feathers. A collection was obtained taking into account several bird species from wet ecosystems in diverse regions of Brazil. For comparison reason, feathers were actively sampled in a riparian forest from the Marins Stream, Piracicaba, Sao Paulo State, using mist nets specific for capturing birds. Biological certified reference materials were used for assessing the quality of analytical procedure. Quantification of chemical elements was performed using the k(0)-INAA Quantu Software. Sixteen chemical elements, including macro and micronutrients, and trace elements, have been quantified in feathers, in which analytical uncertainties varied from 2% to 40% depending on the chemical element mass fraction. Results indicated high mass fractions of Br (max=7.9 mgkg(-1)), Co (max= 0.47 mg kg(-1)), Cr (max =68 mg kg(-1)), Hg (max =2.79 mg kg(-1)), Sb (max= 0.20 mg kg(-1)), Se (max=1.3 mg kg(-1)) and Zn (max =192 mg kg(-1)) in bird feathers, probably associated with the degree of pollution of the areas evaluated. In order to corroborate the use of k(0)-INAA results in biomonitoring studies using avian community, different factor analysis methods were used to check chemical element source apportionment and locality clustering based on feather chemical composition. (C) 2010 Elsevier B.V. All rights reserved.

Variation in the Distribution of Trace Elements in Renal Cell Carcinoma

The development of cancer is a complex, multistage process during which a normal cell undergoes genetic changes that result in phenotypic alterations and in the acquisition of the ability to invade other sites. Inductively coupled plasma optical emission spectroscopy was used to estimate the contents of Al, Ca, Cd, Cr, Cu, Fe, K, Mg, Mn, Na, P, Pb, and Zn in healthy kidney and renal cell carcinoma (RCC), and significant differences were found for all elements. Along with the progression of the malignant disease, a progressive decrease of Cd and K was observed. In fact, for Cd, the concentration in stage T4 was 263.9 times lower than in stage T1, and for K, the concentration in stage T4 was 1.73 times lower than in stage T1. Progressive accumulation was detected for P, Pb, and Zn in stage T4. For P, the concentration in stage T4 was 11.1 times higher than in stage T1; for Pb, the concentration in stage T4 was 232.7 times higher than in T1; and for Zn, the concentration in T4 was 8.452 times higher than in T1. This study highlights the marked differences in the concentrations of selected trace metals in different malignant tumor stages. These findings indicate that some trace metals may play important roles in the pathogenesis of RCC.

Collimated scanning LS-INAA for testing trace elements homogeneity in Brazilian coffee beans

The degree of homogeneity is normally assessed by the variability of the results of independent analyses of several (e.g., 15) normal-scale replicates. Large sample instrumental neutron activation analysis (LS-INAA) with a collimated Ge detector allows inspecting the degree of homogeneity of the initial batch material, using a kilogram-size sample. The test is based on the spatial distributions of induced radioactivity. Such test was applied to samples of Brazilian whole (green) coffee beans (Coffea arabica and Coffea canephora) of approximately I kg in the frame of development of a coffee reference material. Results indicated that the material do not contain significant element composition inhomogeneities between batches of approximately 30-50 g, masses typically forming the starting base of a reference material.

Native bromeliads as biomonitors of airborne chemical elements in a Brazilian restinga forest

Epiphytic bromeliads have been used as biomonitors of air pollution since they have specialized structures in leaves for absorbing humidity and nutrients available in the atmosphere. Leaves of five bromeliad species were collected in the conservation unit Parque Estadual Ilha do Cardoso, Sao Paulo State, Brazil, and analyzed by INAA. Vriesea carinata was the species showing most accumulation, with the highest mass fractions of K, Na, Rb and Zn. Similar results were previously found for the same species collected in the dense ombrophilous forest. Chemical composition of bromeliads provided an indication of the atmosphere status in the conservation unit.

Status of chemical elements in Atlantic Forest tree species near an industrial complex

Environmental quality assessment studies have been conducted with tree species largely distributed in the Atlantic Forest. Leaf and soil samples were collected in the conservation unit Parque Estadual da Serra do Mar (PESM) nearby the industrial complex of Cubatao, Sao Paulo State, Brazil, and analyzed for chemical elements by instrumental neutron activation analysis. Results were compared to background values obtained in the Parque Estadual Carlos Botelho (PECB). The higher As, Fe, Hg and Zn mass fractions in the tree leaves of PESM indicated anthropogenic influence on this conservation unit.

Atlantic forest: A natural reservoir of chemical elements

The accumulation of chemical elements in biological compartments is one of the strategies of tropical species to adapt to a low-nutrient soil. This study focuses on the Atlantic Forest because of its eco-environmental importance as a natural reservoir of chemical elements. About 20 elements were determined by INAA in leaf, soil, litter and epiphyte compartments. There was no seasonality for chemical element concentrations in leaves, which probably indicated the maintainance of chemical elements in this compartment. Considering the estimated quantities, past deforestation events could have released large amounts of chemical elements to the environment.

Laser-induced breakdown spectroscopy and chemometrics for classification of toys relying on toxic elements

Quality control of toys for avoiding children exposure to potentially toxic elements is of utmost relevance and it is a common requirement in national and/or international norms for health and safety reasons. Laser-induced breakdown spectroscopy (LIBS) was recently evaluated at authors` laboratory for direct analysis of plastic toys and one of the main difficulties for the determination of Cd. Cr and Pb was the variety of mixtures and types of polymers. As most norms rely on migration (lixiviation) protocols, chemometric classification models from LIBS spectra were tested for sampling toys that present potential risk of Cd, Cr and Pb contamination. The classification models were generated from the emission spectra of 51 polymeric toys and by using Partial Least Squares - Discriminant Analysis (PLS-DA), Soft Independent Modeling of Class Analogy (SIMCA) and K-Nearest Neighbor (KNN). The classification models and validations were carried out with 40 and 11 test samples, respectively. Best results were obtained when KNN was used, with corrected predictions varying from 95% for Cd to 100% for Cr and Pb. (C) 2011 Elsevier B.V. All rights reserved.